The Holland international has not featured for the Nerazzurri since September after rejecting a request to take a pay cut, although coach Andrea Stramaccioni has long insisted his absence from the team is solely a tactical decision.
Sneijder was dismissed from training for Christmas early, despite Inter having two more games to play before the winter break, and now appears to finally be on his way from the club.
Sneijder, who won the treble with Inter under Jose Mourinho in 2010, has reportedly attracted the interest of Paris Saint-Germain and both Manchester City and Manchester United, but it appears Turkish outfit Galatasaray are leading the chase for his signature.
"Galatasaray announces it has begun negotiations with the FC Internazionale for the transfer of Wesley Sneijder," read a statement on Galatasaray's official website.
"The public will be informed of developments."
Sneijder's wife, actress and television personality Yolanthe Sneijder-Cabau, recently revealed her husband would leave Inter early this month.
"We are about to emigrate," she said just before Christmas. "It should happen in early January and we are looking for a nice place for our family."